The cellular nature of hydrodynamic flame instability

Gutman, Semion; Sivashinsky, G. I.

doi:10.1016/0167-2789(90)90021-g

Cited by 64 publications

(48 citation statements)

References 11 publications

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“…In contrast to periodic boundaries, the crest will always align in the center for reflecting boundary conditions. This is consistent with semi-analytical results (Gutman & Sivashinsky 1990);…”

Section: The Cellular Burning Regime and Its Numerical Simulationsupporting

confidence: 93%

“…This may be interpreted as a hint to increased sensitivity of the cellular flame stabilization to (numerical) noise at low fuel densities; -the evolution of the flame shape tends to a steady state consisting of only one cell filling the entire computational domain. This is consistent with results from semi-analytical and analytical studies based on the Sivashinsky-equation (Gutman & Sivashinsky 1990;Thual et al 1985). The single-cell solution establishes independently of the wavelength of the initial flame perturbation via merging of small cells; -applying a simulation setup of an on average planar flame configuration in a finite computational domain leads to a dependence of the alignment of the finally emerging domain-filling single-cell structure on the boundary conditions imposed transverse to the direction of flame propagation.…”

Section: The Cellular Burning Regime and Its Numerical Simulationsupporting

confidence: 85%

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The cellular burning regime in type Ia supernova explosions

Röpke

Hillebrandt²,

Niemeyer³

2004

A&A

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Abstract. We investigate the interaction of thermonuclear flames in Type Ia supernova explosions with vortical flows by means of numerical simulations. In our study, we focus on small scales, where the flame propagation is no longer dominated by the turbulent cascade originating from large-scale effects. Here, the flame propagation proceeds in the cellular burning regime, resulting from a balance between the Landau-Darrieus instability and its nonlinear stabilization. The interaction of a cellularly stabilized flame front with a vortical fuel flow is explored applying a variety of fuel densities and strengths of the velocity fluctuations. We find that the vortical flow can break up the cellular flame structure if it is sufficiently strong. In this case the flame structure adapts to the imprinted flow field. The transition from the cellularly stabilized front to the flame structure dominated by vortices of the flow proceeds in a smooth way. The implications of the results of our simulations for Type Ia Supernova explosion models are discussed.

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Section: The Cellular Burning Regime and Its Numerical Simulationsupporting

confidence: 93%

Section: The Cellular Burning Regime and Its Numerical Simulationsupporting

confidence: 85%

The cellular burning regime in type Ia supernova explosions

Röpke

Hillebrandt²,

Niemeyer³

2004

A&A

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“…The nonsteady behavior of the solution of the PDE, presumably observed for large values of γ, does not seem to agree with the expectation from the pole-decomposition theory which does not distinguish between small and large values of γ. Joulin and coworkers [6,12] argue that the PDE is therefore not capable of describing the repetitive generation of new "cusps" when γ is large. The appearance of new "cusps" in the computations [5,9] results from the limitations of the numerics. To describe mathematically the experimental observation, specific to large flames [10,11], new models need to be derived.…”

mentioning

confidence: 99%

Stability of Pole Solutions for Planar Propagating Flames: I. Exact Eigenvalues and Eigenfunctions

Vaynblat¹,

Matalon²

2000

SIAM J. Appl. Math.

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Abstract.It is well known that the nonlinear PDE describing the dynamics of a hydrodynamically unstable planar flame front admits exact pole solutions as equilibrium states. Such a solution corresponds to a steadily propagating cusp-like structure commonly observed in experiments. In this work we investigate the linear stability of these equilibrium states-the steady coalescent pole solutions. In previous similar studies, either a truncated linear system was numerically solved for the eigenvalues or the initial value problem for the linearized PDE was numerically integrated in order to examine the evolution of initially small disturbances in time. In contrast, our results are based on the exact analytical expressions for the eigenvalues and corresponding eigenfunctions. In this paper we derive the expressions for the eigenvalues and eigenfunctions. Their properties and the implication on the stability of pole solutions is discussed in a paper which will appear later.

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“…This type of asymmetric cell, with a deep fold in the flame front at one side of the domain would not be compatible with periodic boundaries for this domain width. Asymmetric cells of this type are seen for one case of the solution of the MichelsonSivashinsky equation (Michelson and Sivashinsky 1977), but unlike here, it was later found that this was just a transitory stage and eventually the solution evolved to a single symmetric cell across the domain (Gutman & Sivashinsky 1990). However, for a domain width similar to the one used here (in terms of λ m ) and perturbation wavelength corresponding to our λ = 24 ∼ 2λ m case, Travnikov et al (2000) also found in their Le = 1 calculations that the cell evolved from a half a cell across the domain to a single asymmetric cell.…”

Section: Nonlinear Evolution and Stationary Statesmentioning

confidence: 44%

“…for weak heat releases. Michelson & Sivashinsky (1977,1982 and Gutman & Sivashinsky (1990) solved the evolution equation numerically in wide domains (up 163λ m ) and found the flame evolved to a single very large symmetric stationary cell in the domain, with a sharp cusp or 'fold' at the troughs. For sufficiently large domains they also found that the large cell contained much smaller amplitude cells of average wavelength a few times λ m , which were is a state of constant flux.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

Sharpe

Falle

2006

Combustion Theory and Modelling

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Abstract. Two-dimensional compressible Reactive Navier-Stokes numerical simulations of intrinsic planar, premixed flame instabilities are performed. The initial growth of a sinusoidally perturbed planar flame is first compared with the predictions of a recent exact linear stability analysis, and it is shown the analysis provides a necessary but not sufficient test problem for validating numerical schemes intended for flame simulations. The long-time nonlinear evolution up to the final nonlinear stationary cellular flame is then examined for numerical domains of increasing width. It is shown that for routinely computationally affordable domain widths, the evolution and final state is, in general, entirely dependent on the width of the domain and choice of numerical boundary conditions. It is also shown that the linear analysis has no relevance to the final nonlinear cell size. When both hydrodynamic and thermal-diffusive effects are important, the evolution consists of a number of symmetry breaking cell splitting and re-merging processes which results in a stationary state of a single very asymmetric cell in the domain, a flame shape which is not predicted by weakly nonlinear evolution equations. Resolution studies are performed and it is found that lower numerical resolutions, typical of those used in previous works, do not give even the qualitatively correct solution in wide domains. We also show that the long-time evolution, including whether or not a stationary state is ever achieved, depends on the choice of the numerical boundary conditions at the inflow and outflow boundaries, and on the numerical domain length and flame Mach number for the types of boundary conditions used in some previous works.

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The cellular nature of hydrodynamic flame instability

Cited by 64 publications

References 11 publications

The cellular burning regime in type Ia supernova explosions

The cellular burning regime in type Ia supernova explosions

Stability of Pole Solutions for Planar Propagating Flames: I. Exact Eigenvalues and Eigenfunctions

Nonlinear cellular instabilities of planar premixed flames: numerical simulations of the Reactive Navier–Stokes equations

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